by Monica Yuskaitis, M.A.Ed. 6th Grade Algebra 5 Writing Inequalities 6 ≥ w by Monica Yuskaitis, M.A.Ed. Copyright © 2013 by Monica Yuskaitis

Full Attention to Lesson Ignore Distractions Eyes Front Listen Focus

Objective To be able to write an inequality to represent a condition in the real world. Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Essential Question How can I write an inequality to represent a condition in the real world? Copyright © 2013 by Monica Yuskaitis

We say: h is greater than 6 Vocabulary Greater than (>) – a symbol used to show numbers greater than another. h > 6 We say: h is greater than 6 Copyright © 2013 by Monica Yuskaitis 5

Copyright © 2013 by Monica Yuskaitis Vocabulary Less than (<) – a symbol used to show numbers less than another. 9 < z We say: 9 is less than z. Copyright © 2013 by Monica Yuskaitis 6

Remember! The hungry alligator always eats the largest number. 7 Copyright © 2013 by Monica Yuskaitis

We say: m is greater than or equal to 7 Vocabulary Greater than or equal to (≥) – a symbol used to show numbers greater or equal to another. m ≥ 7 We say: m is greater than or equal to 7 Copyright © 2013 by Monica Yuskaitis 8

Copyright © 2013 by Monica Yuskaitis Vocabulary Less than or equal to (≤) – a symbol used to show numbers less than or equal to another. w ≤ 9 We say: w is less than or equal to 9 Copyright © 2013 by Monica Yuskaitis 9

Copyright © 2013 by Monica Yuskaitis Vocabulary Equals (=) a symbol used to show numbers having the same value. x = y We say: x is equal to y Copyright © 2013 by Monica Yuskaitis 10

Copyright © 2013 by Monica Yuskaitis Vocabulary Not Equal (≠) a symbol used to show numbers having different values. d ≠ 8 We say: d is not equal to 8 Copyright © 2013 by Monica Yuskaitis 11

Which Sign Means Equals? < > ≥ ≠ = ≤ Copyright 2013 by Monica Yuskaitis 12

Which Sign Means greater than? < > ≥ ≠ = ≤ Copyright 2013 by Monica Yuskaitis 13

Which Sign Means less than? < > ≥ ≠ = ≤ Copyright 2013 by Monica Yuskaitis 14

Which Sign Means not equal to? < > ≥ ≠ = ≤ Copyright 2013 by Monica Yuskaitis 15

Which Sign Means greater than or equal to? < > ≥ ≠ = ≤ Copyright 2013 by Monica Yuskaitis 16

Which Sign Means less than or equal to? < > ≥ ≠ = ≤ Copyright 2013 by Monica Yuskaitis 17

Copyright © 2013 by Monica Yuskaitis Let’s Use The Signs 18 Copyright © 2013 by Monica Yuskaitis

Write the Following Correctly 3 ≥ b 3 is greater than or equal to b y is less than or equal to 35 x is not equal to 9 10 plus r is greater than 20 y ≤ 35 x ≠ 9 (10 + r) > 20 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Write the Following Correctly t cubed is equal to 27 y is less than or equal to 75 7 times b is less than 100 12 is greater than or equal to y plus 8 t3 = 27 y ≤ 75 7b < 100 12 ≥ (y + 8) 20 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Looking at Real Life Inequalities 21 Copyright © 2013 by Monica Yuskaitis

The Toy Company

w = weight w ≥ 50 Toy Company A toy company charges an extra fee for toys that weigh 50 or more lbs. w = weight w ≥ 50 If you ordered a toy that weighed 40 lbs would you pay the extra fee? No 40 is not in the solution set. Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Vocabulary Solution Set – the solution set in an inequality is the set of all of the numbers that work for that inequality. w ≥ 50 Numbers not in solution set: 3, 8, 7, 15, 29, 48 Numbers in solution set: 50, 67, 85, 91, 123

Using A Number Line to Graph an Inequality w ≥ 50 10 20 70 40 50 60 30 80 Filled dot means 50 is in the set. Open dot would mean 50 is not part of the solution set.

The Roller Coaster Ride

i = inches i > 48 Roller Coaster You have to be over 48 inches tall to ride the roller coaster. i = inches i > 48 What are some numbers not in the solution set? 10, 20, 33, 47 Name numbers in the solution set? 49, 53, 65, 71 27 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Roller Coaster i > 48 10 20 70 40 50 60 30 80 Open dot would mean 48 is not part of the solution set.

Airplane Ride

y = years y ≤ 3 Airplane Ride Children 3 years old or younger can ride the airplane for free. y = years y ≤ 3 What are some numbers not in the solution set? 5, 7, 9, 12,15 Name numbers in the solution set? 3, 2 1/2, 1, .5 30 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Airplane Ride y ≤ 3 1 2 7 4 5 6 3 8 Filled dot means 3 is in the set.

Copyright © 2013 by Monica Yuskaitis It Is Your Turn! 32 Copyright © 2013 by Monica Yuskaitis

m = Mike’s age Age Question Mike is at least 1 year older than his sister Mary. Mary is 4 years old. How old could Mike be? m = Mike’s age Write an inequality expression and then graph it on a number line. Go to next slide for answer. 33 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Age Question Mike is at least 1 year older than his sister Mary. Mary is 4 years old. How old could Mike be? m ≥ (4+1) 1 2 7 4 5 6 3 8 34 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

p = points scored Soccer Game Susan scored fewer than 7 points in the soccer game. How many points could she score? p = points scored Write an inequality expression and then graph it on a number line. Go to next slide for answer. 35 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Age Question Susan scored fewer than 7 points in the soccer game. How many points could she score? p < 7 1 2 7 4 5 6 3 8 36 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Book Cost Gabriel called the book store to get the price of a science book he wanted to buy. When he asked for the price, he was told it would cost at least $5. b = book cost Write an inequality expression and then graph it on a number line. Go to next slide for answer. 37 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Book Cost Gabriel called the book store to get the price of a science book he wanted to buy. When he asked for the price, he was told it would cost at least $5. b ≥ 5 1 2 7 4 5 6 3 8 38 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Checking For Understanding 39 Copyright © 2013 by Monica Yuskaitis

What inequality does this number line show? 10 20 70 40 50 60 30 80 n _______ ≥ 30

What inequality does this number line show? 10 20 70 40 50 60 30 80 n _______ < 70

What inequality does this number line show? 1 2 7 4 5 6 3 8 n _______ < 3

What inequality does this number line show? 1 2 7 4 5 6 3 8 n _______ ≥ 1

Write True or False 10 7 11 8 9 false true false true true These numbers are solutions to r ≤ 9 10 7 11 8 9 false true false true true Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Write True or False 5 6 2 8 9 false true false true true These numbers are solutions to s > 5 5 6 2 8 9 false true false true true 45 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Write True or False f = 5 f = 6 f = 9 f = 2 f = 7 true true false true These numbers are solutions to 6 ≥ f f = 5 f = 6 f = 9 f = 2 f = 7 true true false true false 46 Copyright © 2013 by Monica Yuskaitis Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Problem Solving 47 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Ice Copyright © 2013 by Monica Yuskaitis

Analysis Representation Resolution Problem Solving Steps What information do you need? What is the problem asking you to find out? Is the answer going to be larger or smaller? Representation What strategies will you use? What operations will you use? How many steps are there and in what order must you do them? How will you solve the problem? Did you check your answer? Does your answer make sense? Resolution Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Water freezes at and below 32oF. Write an inequality and graph this situation. f ≤ 32 10 20 70 40 50 60 30 80 Copyright © 2013 by Monica Yuskaitis

You deserve flowers! 51 Copyright © 2013 by Monica Yuskaitis

Don’t forget to rate this lesson! After you click, make sure you sign in! Click Here! Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Copyright Notice This presentation is copyrighted. You have the right to use or even alter the slides for your own personal use in the classroom or with individuals. However, you do not have the right to copy and give or to sell this product to anyone. Severe penalties are in place should you decide to do so. Copyright © 2013 by Monica Yuskaitis

Credits Contact: Clipart from clipart.com Written by Monica Yuskaitis To view 400 more math presentations like this one Contact: http://www.teacherspayteachers.com/Store/Effective-Math-Lessons Copyright © 2013 by Monica Yuskaitis 54